Surface freezing and a two-step pathway of the isotropic-smectic phase transition in colloi

We study the kinetics of the isotropic-smectic phase transition in a colloidal rod/polymer mixture by visualizing individual smectic layers. First, we show that the bulk isotropic-smectic phase transition is preceded by a surface freezing transition in whi

Surfacefreezingandatwo-steppathwayoftheisotropic-smecticphase

transitionincolloidalrods

ZvonimirDogic

IFF/WeicheMaterie,ForschungszentrumJ¨ulich,J¨ulich,D-52425Germany

(Dated:February2,2008)

Westudythekineticsoftheisotropic-smecticphasetransitioninacolloidalrod/polymermixturebyvisualizingindividualsmecticlayers.First,weshowthatthebulkisotropic-smecticphasetran-sitionisprecededbyasurfacefreezingtransitioninwhichaquasitwo-dimensionalsmecticphasewetstheisotropic-nematicinterface.Next,weidentifyatwostepkineticpathwayfortheformationofabulksmecticphase.Inthe rststepametastableisotropic-nematicinterfaceisformed.Thisinterfaceiswettedbythesurfaceinducedsmecticphase.Inthesubsequentstep,smecticlayersnucleateatthissurfacephaseandgrowintotheisotropicbulkphase.

PACSnumbers:64.70.Md82.70.D

arXiv:cond-mat/0308556v1 [cond-mat.soft] 26 Aug 2003

Colloidswithhardcorerepulsiveinteractionsareoftenstudiedduetothesimplicityandgeneralityoftheirintermolecularpotential.Asaresultofthesestudies,theequilibriumphasediagramofhardrodsandspheresiswellunderstoodatthepresenttime[1,2,3,4].However,muchlessisknownaboutthekineticpathwaysofphasetransitionsinthesesystemsDirectvisualizationofcolloidsinasystemundergoingphasetransitionhaveprovidedapowerfultooltostudygeneralaspectsofphasetransitionkinetics8].Inthispaperwestudythekineticsoftheisotropic-smecticphasetransitionbydirectlyvisualizingindividualsmecticlayersinaphaseseparatingsample.Asamodelsystemofcol-loidalrodsweuseamonodispersesuspensionoffdvirusWeelucidateakineticpathwayofunex-pectedcomplexity.Theexistenceofsurfacefreezingandametastableisotropic-cholestericphasetransi-tionsisdiscoveredandtheirin uenceonthekineticpathwayisdiscussed.Becausethebehaviorofthefd/Dextranmixtureisdeterminedbystericinterac-tionsandsinceallmoleculesincludinglowmolecu-larweightthermotropicshaveastericcorethere-sultsreportedinthispaperarelikelytobequitegeneral.Inaddition,ourresultsmightbepertinenttounderstandingthedynamicsofamphiphilicmem-branes2Dsmecticsystemssurfacefreezingandwettingtransitionsandselfassem-blednano-structures[15].

Ithasbeenknownforalongtimethatsurfacefreezing/meltingcandramaticallyalterthenucle-ationrateandthekineticpathwayofaphasetran-sition.Ononehand,mostsubstancesexhibitsur-facemelting.Inthiscasealiquidsurfacewetsthecrystallinebulkphase.Itfollowsthatcrys-talsmeltfromthesurfaceinwardsandthereforeitisdi culttoprepareasuperheatedmetastablesolidOntheotherhand,surfacefreez-ingisobservedinveryfewsystems,mostnotablythermotropicliquidcrystals,alkanesandsurfactantmesophases[12,13,Uponsupercoolingthese

materials,theorderedphasenucleatesatthefrozeninterfaceandpropagatestowardsthebulkphase.Therefore,itisdi culttosupercoolliquidsthatex-hibitsurfacefreezing[19].

Anotherfactorthatcana ectthenucleationrateofatransitionsisthepresenceofmetastablephasesForexample,recentsimulationspredictthatthefreeenergybarrierforthefor-mationofproteincrystalsisgreatlyreducedwhenametastablegas-liquidphasetransitionislocatedinavicinityofastableliquid-solidphasebound-aryInthiscasethenucleationofproteincrys-talsproceedsintwosteps.Inthe rststepadensemetastabledropletassociatedwiththegas-liquidphasetransitionisformed,whileinthesubsequentsteptheproteincrystalnucleateswithinthisdroplet.Inthispaperweshowthatbothsurfacefreezingandmetastablephasesareimportantforunderstandingthekineticsoftheisotropic-smecticphasetransition.Bacteriophagefdisasemi- exibleviruswithcon-tourlengthof880nm,diameterof7nmandper-sistencelengthof2200nm.Itwaspreparedaspreviouslydescribedanddialyzedagainstbu erofknownionicstrength(190mMNacl,10mMTris,pH=8.10).Thephasediagramoftherod-polymermixturewasmeasuredaccordingtothepublishedprocedure[9].Allthesamplesarepreparedinametastable/unstableisotropicphasebyshearmelt-inganyexistingstructureandsamplesareplacedintorectangularcapillaries(VitroCom,MountainLakes,NJ).Nucleationandgrowthoftheorderphaseisobservedwithanopticalmicroscope(ZeissAxioPlan2)equippedwithDICoptics.AllimagesarerecordedwithacooledCCDcamera(AxioCamZeiss)

Atzeropolymerconcentrationfdisagoodmodelsystemofhardrodsandformsastableisotropic(I),cholesteric(Ch)andsmectic(S)phaseswithincreas-ingconcentrationinagreementwiththeoreticalpre-dictions21].EquilibriumI-Sphasetransitionisobservedinamixtureofrod-likefdvirusesandnon-

We study the kinetics of the isotropic-smectic phase transition in a colloidal rod/polymer mixture by visualizing individual smectic layers. First, we show that the bulk isotropic-smectic phase transition is preceded by a surface freezing transition in whi

FIG.1:Thecoexistenceconcentrationsofanimmisci-blefd-Dextranmixture.TheY-axesshowsconcentra-tionandosmoticpressureofDextraninthephasethatcoexistswithrod-richliquidcrystallinephase(droplets)whoseconcentrationisshownontheX-axis.Numbers1through4indicateregionswheredi erentphasebehav-iorsareobserved.Imagesof

thestructuresobservedintheseregionsareshowninFig.2.Stablesurfacesmec-ticphasewetstheisotropic-nematicinterfaceinregion2.Colloidalmembranesarestableinregion3.Inset:Thecompletephasediagramoffd/Dextranmixture.Tielinesalongwhichthephaseseparationproceedsareindi-catedbydashedlines.Regionsoftheisotropic-nematic(I-N)andisotropic-smectic(I-S)coexistenceareindi-cated.

adsorbingpolymerDextran.ThephasediagramofthismixtureisshownintheinsetofFig.1.Addingnon-adsorbingpolymertofdsuspensionproducesef-fectiveattractiveinteractionsbetweenfdrods[22].ThemainconsequenceofthisattractivepotentialonthephasebehaviorofarodlikesystemistowidentheI-Chcoexistenceconcentrationswiththepolymerpreferentiallypartitioningintotheisotropicphase[23].Sincetheinteractionsinthefd/polymermixturesaretemperatureindependent,allphasetransitionsareentropicallydriven.Inthe rstpartofthepaperwedescribetheequilibriumstructuresrelatedtothesurfacefreezingobservedinregion2ofthephasediagram.Inthesecondpartofthepa-perwedescribeoneofthekineticpathwaysofphaseseparationobservedinregion3.

Atrodconcentrationsbelow235mg/ml(region1

FIG.2:Imagesandschematicrepresentationsofdi er-entstructuresobservedinthefd/Dextranmixture.(a)Anisotropicnematicdropletinthepolymerrichback-ground.Con gurationofrodsinshownin gurec.(b)Nematicdropletwithsurfacesmecticphase.Imageisformedbyfocusingonthemidplaneofthetactoids.The3Dstructureisanobjectofrevolutionaboutthelongaxis.Aschematicrepresentationofanematicdropletwithsurfaceinducedsmecticphaseisshowninimaged.(e)Colloidalmembraneswhichhomogeneouslynucleatefromisotropicphase.Thebottomleftdiskliesintheplaneoftheimagewhiletheothertwolineperpendicu-lartotheplaneoftheimage(f)Twistedribbonwhichisidenticaltocolloidalmembraneexceptthatthatitiselongatedalongthetwistdirections(g)Bulkisotropic-smecticphasecoexistence.Scalebarsindicate3µm.

inFig.1aandb),nematicdroplets(tactoids)forminanisotropicbackground(Fig.2a).Polarizationmicroscopyindicatesthatthecon gurationofrodsinthenematictactoidisasshowninFig.2c.Whencon nedtoasmallvolumethecholestericorderisnotabletodevelop;thereforeweobserveonlyun-woundnematicphasewithinaindividualtactoid.Athigherrodconcentrations(region2inFig.1)weobservedropletsthathavethesameanisotropicshape.Microscopyindicatesthattheinteriorofthesedropletsisstillnematic.However,eachdroplet

We study the kinetics of the isotropic-smectic phase transition in a colloidal rod/polymer mixture by visualizing individual smectic layers. First, we show that the bulk isotropic-smectic phase transition is preceded by a surface freezing transition in whi

FIG.3:Imageofamacroscopicallyphaseseparatedisotropic-nematicinterfaceswhichexhibitsurfacefreez-ing.Theconcentrationsofthecoexistingisotropicandnematicphasesarecfd=242mg/mlandcdex=51.5mg/ml.Densenematicphaseisbelowtheimageplanewhiletheisotropicphaseisabovetheimage.Thethick-nessofthesurfaceinducedsmecticphaseisfewhundrednm.Thesurfacestructureshow

hereisidenticaltothesurfaceoftactoidsshowninFig.2d.Apairofdisloca-tiondefectsisclearlyvisibleintheimage.Scalebarsindicate5µm.

hasacorrugatedI-Ninterfacewherethelengthofeachridgealongthedroplet’slongaxisisapproxi-matelyoneviruslong.Asthetactoidscoalesceandincreaseinsize,thesurfacecorrugationsarealwayscon nedtoanarrowlayerofwellde nedthicknesslocatedattheI-Ninterface.Thisimpliesthattheformationofcorrugationsisapurelysurfacee ect.Theseobservationsleadustoconclusionthatthereexistsasurface-inducedquasi2DsmecticphasethatwetstheI-Ninterface.Theridgesobservedattheinterfaceareindividuallayersofthesurface-inducedsmecticphase.Aschematicrepresentationofasec-tionofacorrugatedtactoidisshowninFig.2d.Thesurfacesmecticphaseisobservedaboveanfdcon-centrationof235mg/mlwhilethebulkI-Sphasetransition(region4)isobservedat255mg/ml.

Afterafewhours,thefd/Dextranmixturepre-paredinregion2completelyphaseseparateswithdensernematictactoidscoalescingandsettlingtothebottomofthesample.InthiscaseamacroscopicI-Ninterfaceisformed.Thismakesitpossibletofo-cusontheinterfaceanddirectlyobservethesurfaceinducedsmecticphase(Fig.3).Weconcludeourdescriptionofthesysteminregion2bynotingthattherearenotheoreticalpredictionsofthesurface-inducedsmecticphaseinrod/polymermixture.Weexpectthatsuchphaseisaresultofnon-monotonicdensitypro lesacrosstheI-Ninterface[24].Addi-tionally,inthefd/polymersystemrodsinthesurfacefrozenlayerlieintheplaneoftheinterface.Thisisincontrasttomolecularsystemswhichexhibitsur-facefreezingwhereanisotropicmoleculesareeithertiltedorperpendiculartotheinterface[12,13].Wenowturnourattentiontoregion3ofthephasediagram.Rightaftermixingthesample,inadditiontotheformationofnematicdropletswithasurfacesmectic,weobserveself-assemblyofrodsintodisk-likeorribbon-likestructures(Fig.2eandf).Thethicknessofthediskcorrespondstothelengthofa

FIG.4:Imagesofstructuresobservedinregion3ofthephasediagramafterthesamplehasbeenequilibratedforafewdays.Forimagesaandbcfd=254mg/mlandcdex=53.5mg/mlwhileforimagescanddcdex=56mg/mlandcfdisundetermined.(a)Nematicdropletwithasurfacefrozensmecticphase.Surfacesmecticphaseactsasanucleationsitefortheformationofcol-loidalmembranes.(b)Twistedsmecticribbonnucleatesatthesurfacesmecticphaseandgrowsintotheisotropicbulkphase(c)DICimageofalarge(35µmdiameter)isolatedcolloidalmembraneinwhichrodslieperpendic-ulartotheimageplane.Correspondinglythemembraneshowsnobirefringenceundercrossedpolarizers.(d)Po-larizationimageofacolloidalmembraneinwhichrodslieintheplaneoftheimage.Directionsofpolarizerandanalyzerareindicatedbywhitearrows.Scalebarsindicate5µm.

singlerod.Whenviewedfromaboveadiskshowsnobirefringencewhilefromthesideitshowsmaxi-mumbirefringencewhenorientedat45owithrespecttothepolarizerandanalyzer(Fig.4d).Therefore,polarizationmicroscopyshowsthatdisksarecom-posedofamonolayerofalignedrodsinthesmectic-Acon guration.Wecalltheseself-assembleddiskscolloidalmembranesbecauseoftheirsimilaritytoamphiphilicmembranes.Smallhomogeneouslynu-cleatedmembranes(Fig.2e)growbycoalescinglat-erallytoformlarge40µdiameterisolatedmem-branes(Fig.4c)[9].Thissuggeststhatanisolatedcolloidalmembraneandnotabulksmecticphaseistheequilibriumstructureinregion3.Polarizationmicroscopyindicatesthattwistedribbonsareiden-ticaltodisksexceptthattheyhaveatwistalongtheirlongaxisduetothechiralnatureoffd[25].Weexpectthatthefreeenergydi erencebetween

We study the kinetics of the isotropic-smectic phase transition in a colloidal rod/polymer mixture by visualizing individual smectic layers. First, we show that the bulk isotropic-smectic phase transition is preceded by a surface freezing transition in whi

thesetwomorphologiesissmallandwillexaminetheirrelativestabilityelsewhere.

Realspaceimagesenablesustostudytheki-neticpathwayfortheformationofcolloidalmem-branes.Theycaneitherhomogeneouslynucleatefromthemetastableisotropicsuspensionorcanhet-erogeneouslynucleateatthesurface-inducedsmecticphase(Fig.4aandb).Acolloidalmembranenucle-atedattheinterfacegrowsintotheisotropicphaseeitherasatwistedribbonora atdisk.Overape-riodofafewdaystwistedribbonscanreachalengthsofseveralhundredsmicrons.Fluorescenceimagesindicatethattherearenorodsintheisotropicsolu-tion.Thereforecolloidalmembranes(ribbons)mustelongateduetorodsthatdi usefromametastablenematicphasethroughasurfacesmectictoamorestablecolloidalmembrane.Thefactthatthereisatransportofrodsacrosstheinterfaceshowsthatthecolloidalmembranesarestructureswithlowerfreeenergythanthenematicphaseorbulksmecticphase.Atlowerdegreesofsupercoolingwemostlyobserveheterogenoussurfaceinducednucleationin-steadofhomogeneousnucleationofcolloidalmem-branes.Thisshowsthatatwo-stepkineticpathwayhasalowernucleationbarrierfortheformationofcolloidalmembranes.Tosummarize,thephasesep-arationinregion3ofthephasediagramproceedsintwosteps.Inthe rststepontimescaleofsecondstominutesweobservetheformationofnematictac-toidswithsurfacesmecticphaseidenticaltothoseobservedinregion2.However,thesetactoidsaremetastable.Inthesecondslowsteponatimescaleofhourstomonthsweobservethenucleationofcol-loidalmembranesatthesurfacefrozensmecticphaseandtheirsubsequentgrowthintotheisotropicphase.Afewcommentsareinorderregardingthestruc-turesobservedinregion3.First,toourknowledgethisisthe rsttimethatnon-amhiphilicobjectswithverysimpleexcludedvolumeinteractionshavebeenselfassembledinto2Dmembrane-like(Fig.4c)and1Dpolymerlikestructures(Fig.2f)[26].Wespec-ulatethatthesestructuresarestabilizedbyprotru-sionlike uctuations[27].Second,itseemsplau-siblethatisolatedcolloidalmembranesobservedinregion3arehighlyswollenlamellarphasesprevi-ouslyobservedinmixturesofnematicfdandhardspheres[4].Theswellingofthelamellarphaseis

predictedtheoretically,buthasyettobeobservedinexperiments[28].Third,astheosmoticpres-sureisincreasedthereisatransitiontoregion4inwhichsmallcolloidalmembranesirreversiblystackupontopofeachothertoformelongated laments(Fig.2g).Thenatureofthetransitionfromiso-latedmembranestoasmecticphaseremainsun-explored.Fourth,uallythereversee ectisob-servedpathwayswhereastablenucleusiswettedbyametastablephase[5,29]

Inconclusion,therearetwoimportantresultsthatcanbededucedfromourexperiments.The rstsur-prisingresultisthatarod/polymermixtureexhibitssurfacefreezinginwhichaquasi2DsmecticphasewetstheI-Ninterface.Thise ectoccursatrodcon-centrationof235mg/mlwhilebulkI-Sphasetran-sitionoccursat255mg/ml.Toourknowledgethisisthe rsttimethatthesurfacefreezinghasbeendirectlyvisualizedinasystemwhosephasebehaviorisdominatedbyentropicrepulsiveinteractions.Thesecondresultofthisworkistodemonstratethere-lationshipbetweenthesurfacefreezingandthebulkisotropic-smecticphasetransition.Acomplextwostepkineticpathwayforthenucleationofthesmec-ticphaseoutoftheisotropicsolutionhasbeeniden-ti ed.Inthe rststepametastablenematicdropletwithasurfacefrozensmecticphasenucleatesintheisotropicsolution.Inthenextstepisolatedmono-layers(colloidalmembranes)ofsmecticphasenucle-ateatthesurfacesmecticphaseandsubsequentlygrowintotheisotropicphase.Duetothesimplicityandgeneralityoftheexcludedvolumeinteractionswhichdominatethephasebehavioroffd/Dextranmixture,theresultspresentedhereshouldberele-vanttoamuchwiderclassofsystemsthanthosestudiedhere.

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